Experimental Mathematics

Central binomial sums, multiple Clausen values, and zeta values

Jonathan Michael Borwein, David J. Broadhurst, and Joel Kamnitzer

Abstract

We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apery sums). The study of nonalternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio.

Article information

Source
Experiment. Math., Volume 10, Issue 1 (2001), 25-34.

Dates
First available in Project Euclid: 30 August 2001

Permanent link to this document
https://projecteuclid.org/euclid.em/999188418

Mathematical Reviews number (MathSciNet)
MR1 821 569

Zentralblatt MATH identifier
0998.11045

Subjects
Primary: 11Mxx: Zeta and $L$-functions: analytic theory
Secondary: 05Axx: Enumerative combinatorics {For enumeration in graph theory, see 05C30} 11Bxx: Sequences and sets 33Bxx: Elementary classical functions

Keywords
binomial sums multiple zeta values log-sine integrals Clausen's function multiple Clausen values polylogarithms Apéry sums

Citation

Borwein, Jonathan Michael; Broadhurst, David J.; Kamnitzer, Joel. Central binomial sums, multiple Clausen values, and zeta values. Experiment. Math. 10 (2001), no. 1, 25--34. https://projecteuclid.org/euclid.em/999188418


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